Question 713437


First let's find the slope of the line through the points *[Tex \LARGE \left(5,6\right)] and *[Tex \LARGE \left(7,10\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(5,6\right)]. So this means that {{{x[1]=5}}} and {{{y[1]=6}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(7,10\right)].  So this means that {{{x[2]=7}}} and {{{y[2]=10}}}.



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(10-6)/(7-5)}}} Plug in {{{y[2]=10}}}, {{{y[1]=6}}}, {{{x[2]=7}}}, and {{{x[1]=5}}}



{{{m=(4)/(7-5)}}} Subtract {{{6}}} from {{{10}}} to get {{{4}}}



{{{m=(4)/(2)}}} Subtract {{{5}}} from {{{7}}} to get {{{2}}}



{{{m=2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(5,6\right)] and *[Tex \LARGE \left(7,10\right)] is {{{m=2}}}



Now let's use the point slope formula:



{{{y-y[1]=m(x-x[1])}}} Start with the point slope formula



{{{y-6=2(x-5)}}} Plug in {{{m=2}}}, {{{x[1]=5}}}, and {{{y[1]=6}}}



{{{y-6=2x+2(-5)}}} Distribute



{{{y-6=2x-10}}} Multiply



{{{y=2x-10+6}}} Add 6 to both sides. 



{{{y=2x-4}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(5,6\right)] and *[Tex \LARGE \left(7,10\right)] is {{{y=2x-4}}}